Yeah, it was covered in Genesis ...
Genesis 9:2, 3
2 The fear and dread of you will fall upon all the beasts of the earth and all the birds of the air, upon every creature that moves along the ground, and upon all the fish of the sea; they are given into your hands.
3 Everything that lives and moves will be food for you. Just as I gave you the green plants, I now give you everything.
NOTE ...
“Just as I gave you the green plants, I NOW give you everything.”
I always took it to mean something much more than God granting Adam and his progeny the right to keep pets.